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M.: The Tableau Prover Generator MetTeL2
, 2012
"... Abstract. This paper introduces MetTeL2, a tableau prover generator producing Java code from the specification of a tableau calculus for a logical language. MetTeL2 is intended to provide an easy to use system for non-technical users and allow technical users to extend the generated implementations. ..."
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Abstract. This paper introduces MetTeL2, a tableau prover generator producing Java code from the specification of a tableau calculus for a logical language. MetTeL2 is intended to provide an easy to use system for non-technical users and allow technical users to extend the generated implementations. 1
An Abstract Tableau Calculus for the Description Logic SHOI Using Unrestricted Blocking and Rewriting
"... Abstract This paper presents an abstract tableau calculus for the description logic SHOI. SHOI is the extension of ALC with singleton concepts, role inverse, transitive roles and role inclusion axioms. The presented tableau calculus is inspired by a recently introduced tableau synthesis framework. T ..."
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Abstract This paper presents an abstract tableau calculus for the description logic SHOI. SHOI is the extension of ALC with singleton concepts, role inverse, transitive roles and role inclusion axioms. The presented tableau calculus is inspired by a recently introduced tableau synthesis framework. Termination is achieved by a variation of the unrestricted blocking mechanism that immediately rewrites terms with respect to the conjectured equalities. This approach leads to reduced search space for decision procedures based on the calculus. We also discuss restrictions of the application of the blocking rule by means of additional side conditions and/or additional premises. 1
Terminating tableau calculi for modal logic K with global counting operators
"... This paper presents the first systematic treatment of tableau calculi for modal logic K with global counting operators. Using a recently introduced tableau synthesis framework we establish two terminating tableau calculi for the logic. Whereas the first calculus is a prefix tableau calculus, the sec ..."
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Cited by 3 (3 self)
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This paper presents the first systematic treatment of tableau calculi for modal logic K with global counting operators. Using a recently introduced tableau synthesis framework we establish two terminating tableau calculi for the logic. Whereas the first calculus is a prefix tableau calculus, the second is a refinement that internalises the semantics of the logic without using nominals. We prove the finite model property for the logic and show that adding the unrestricted blocking mechanism does not break soundness and completeness of the calculi and ensures termination in both cases. We have successfully implemented the prefix tableau calculus in the MetTeL2 tableau prover generation platform. Keywords: property. modal logic, hybrid logic, tableau, counting operators, finite model 1
MetTeL2: Towards a tableau prover generation platform
- In these proceedings
, 2012
"... This paper introduces MetTeL 2, a tableau prover generator producing Java code from the specification of a logical syntax and a tableau calculus. It is intended to provide an easy to use system for non-technical users and allow technical users to extend the generated implementations. 1 ..."
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This paper introduces MetTeL 2, a tableau prover generator producing Java code from the specification of a logical syntax and a tableau calculus. It is intended to provide an easy to use system for non-technical users and allow technical users to extend the generated implementations. 1
A Refined Tableau Calculus with Controlled Blocking for the Description Logic SHOI
"... Abstract The paper presents a tableau calculus with several refinements for reasoning in the description logic SHOI. The calculus uses non-standard rules for dealing with TBox statements. Whereas in existing tableau approaches a fixed rule is used for dealing with TBox statements, we use a dynamical ..."
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Abstract The paper presents a tableau calculus with several refinements for reasoning in the description logic SHOI. The calculus uses non-standard rules for dealing with TBox statements. Whereas in existing tableau approaches a fixed rule is used for dealing with TBox statements, we use a dynamically generated set of refined rules. This approach has become practical because reasoners with flexible sets of rules can be generated with the tableau prover generation prototype MetTeL. We also define and investigate variations of the unrestricted blocking mechanism in which equality reasoning is realised by ordered rewriting and the application of the blocking rule is controlled by excluding its application to a fixed, finite set of individual terms. Reasoning with the unique name assumption and excluding ABox individuals from the application of blocking can be seen as two separate instances of the latter. Experiments show the refinements lead to fewer rule applications and improved performance. 1
MetTeL 2 : Towards a prover generation platform (system description) (2012), available at http://www. mettel-prover.org/papers/MetTeL2SysDesc.pdf
"... Abstract This paper introduces MetTeL2, a tableau prover generator producing Java code from the specifications of a logical syntax and a tableau calculus. It is intended to provide an easy to use system for non-technical users and allow technical users to extend the implementation of generated prove ..."
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Abstract This paper introduces MetTeL2, a tableau prover generator producing Java code from the specifications of a logical syntax and a tableau calculus. It is intended to provide an easy to use system for non-technical users and allow technical users to extend the implementation of generated provers. 1
Tableau Development for a Bi-Intuitionistic Tense Logic ⋆
"... Abstract. The paper introduces a bi-intuitionistic logic with two modal operators and their tense versions. The semantics is defined by Kripke models in which the set of worlds carries a pre-order relation as well as an accessibility relation, and the two relations are linked by a stability conditio ..."
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Abstract. The paper introduces a bi-intuitionistic logic with two modal operators and their tense versions. The semantics is defined by Kripke models in which the set of worlds carries a pre-order relation as well as an accessibility relation, and the two relations are linked by a stability condition. A special case of these models arises from graphs in which the worlds are interpreted as nodes and edges of graphs, and formulae represent subgraphs. The pre-order is the incidence structure of the graphs. These examples provide an account of time including both time points and intervals, with the accessibility relation providing the order on the time structure. The logic we present is decidable and has the effective finite model property. We present a tableau calculus for the logic which is sound, complete and terminating. The MetTel system has been used to generate a prover from this tableau calculus. 1
Modal Satisfiability via SMT Solving
"... Modal logics extend classical propositional logic, and they are robustly decidable. Whereas most existing decision procedures for modal logics are based on tableau constructions, we propose a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers. ..."
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Modal logics extend classical propositional logic, and they are robustly decidable. Whereas most existing decision procedures for modal logics are based on tableau constructions, we propose a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers. Soundness, completeness, and termination of the procedures can be proved in a uniform and elementary way for the basic modal logic and some extensions.
Modal Tableau Systems with Blocking and Congruence Closure
"... Abstract. Our interest in this paper are semantic tableau approaches closely related to bottom-up model generation methods. Using equality-based blocking techniques these can be used to decide logics representable in first-order logic that have the finite model property. Many common modal and descri ..."
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Abstract. Our interest in this paper are semantic tableau approaches closely related to bottom-up model generation methods. Using equality-based blocking techniques these can be used to decide logics representable in first-order logic that have the finite model property. Many common modal and description logics have these properties and can therefore be decided in this way. This paper integrates congruence closure, which is probably the most powerful and efficient way to realise reasoning with ground equations, into a modal tableau system with equality-based blocking. The system is described for an extension of modal logic K characterised by frames in which the accessibility relation is transitive and every world has a distinct immediate predecessor. We show the sys-tem is sound and complete, and discuss how various forms of blocking such as ancestor blocking can be realised in this setting. Though the in-vestigation is focussed on a particular modal logic, the modal logic was chosen to show the most salient ideas and techniques for the results to be generalised to other tableau calculi and other logics. 1
